Recent advances in the Human Genome Project and high throughput technologies have enabled researchers to study the etiology of complex diseases comprehensively. A large amount of data that have been generated have posed many interesting statistical issues. We propose to continue research on family studies from the previous grant entitled "Methods for Age at Onset Data in Genetic Epidemiology" (AG 14358). The research includes the development of semi-parametric methods for aggregation analysis and for the estimation of marginal cumulative risk for carriers and non-carriers when the susceptible genes are genotyped only on a subset of family members, usually the index subjects of the family. The primary outcomes of interest are the ages at onset for the family members, for which the modem theory of counting processes will be applied to deal with such correlated failure time data. This research is directly motivated by the two-case-control family studies of early onset breast cancer conducted at the Fred Hutchinson Cancer Research Center. In these studies, breast cancer susceptible genes BRCA1/BRCA2 were genotyped on a subset of cases and controls while comprehensive information such as medical history and oral contraceptive usage have been collected on all study participants and their female relatives. We will analyze these data as an illustration for the proposed methods. We also propose to develop statistical methods for the analysis of loss of heterozygosity (LOH) or allelic loss, which is defined as a complete or partial signal reduction of one of the two corresponding alleles in the matching tumor DNA. LOH is one of the most widely used methods for assessing the genomic instability and localizing the tumor suppressor genes. The mathematical representation of the LOH status at an informative marker is 0/1 for retention or loss of heterozygosity. We propose to apply the survival analysis techniques to deal with the increasingly large number of genetic markers, in that the chromosome can be considered as a "time" axis starting from the centromere to the telomere and the markers on the chromosome as the "inspection times". We will develop semi- and non-parametric methods for comparing the LOH profiles between two samples such as two types of breast cancer and for regression analysis of covariates such as expression of p53 gene on the marginal and local dependency analysis of LOHs. We will apply proposed methods to the genome-wide LOH analysis for the lobular and ductal breast cancers.